The technique of dynamic relaxation is invoked in analyzing the nonlinear bending of circular plates of linear elastic material and variable profile subjected to a uniformly distributed lateral loading. Results for clamped plate with exponential profile and for pinned edged plates with linear profile are presented. Comparison of these results for a uniform plate with the available results shows excellent correlation ascertaining the efficiency of the technique. The results from extensive numerical experiments are presented in such a form as to reflect the effect of variable profile, in particular, on the boundary layer phenomenon. Approximate estimates for the values of the important parameters, i.e., the time increment and damping coefficients, are suggested.